Best way to build stud wall where joists run parallel?

We are working on our basement and have finished building our first wall and now are turning to finish our second. The first wall ran perpendicular to the joists so attaching the top plate was no issue--everything (for once) went according to plan!

The second stud wall we need to construct, however, runs parallel to the joists up against a cinderblock wall (the wall separates two basement rooms from each other). So basically this stud wall is going up against a cinderblock wall and I think I'll need to add some blocking between the joists to attach the top plate to--BUT, here's the rub: There is no second joist to attach the blocking to since the cinderblock wall goes all the way up where the fireplace bottom sits on it.

That may be a bit confusing so let me describe it a different way. If you were standing where this wall needs to be built and you looked up into the joist cavity, you would see a joist on your right and cinderblock on your left. So How am I going to install this blocking? Or is there a better way to do it? I'm going to need electrical on that wall so I don't think I can just using furring strips (plus I don't thin the wall is straight ).

Okay let me attach a picture since I think I've convoluted this question beyond the point of words at this point. This should help:

Thanks for the quick response Jim, do you mean attach the wall studs to the concrete wall? If so, then for the anchors and nails would you go the long way (like through the 3.5" part?) through the studs? i need to hve electrical boxes and such on that wall so i don't think I could just attach the 2x4s striaght the the wall if they are only going to stand off 1.5" right?

To attach the studs to the wall you can use some scraps of 2x4 at 4' horizontal intervals at the top and bottom. Turn the scraps flat against the wall, secure them to the wall with anchors then level (plumb) the new studwall and nail into the scraps that are attached to the wall. I have also used small "L" tabs found in the Stimpson section of big blue and nailed them into the stud then shot them into the concrete using a Hilti nail. Faster, if you have the tools.

If the blocking was wedged between concrete block wall and nailed to the joist, I think you could attach wall to the blocking. Add a little polyurethane glue between wall and blocking if it makes you feel better. It's not load bearing and not going anywhere.

INteresting. I don't think I have ever seen a floor without a rim joist around the outside perimeter for the floor to rest on it. You will have to provide a rim joist by using TapCon screws or RamSet anchors.

Since there isn't another joist, just use some concrete screws, tapcons, anchors, whatever you want, and create a false joist with a 2x4.

It just has to be there for the blocking to tie into, so just make sure the bottom of the 2x4 is flush with the joist, and you could even end nail your blocking to this 2x4, before anchoring it to the block wall.

Personally I would put some sill gasket between the cinderblock and the false joist, and I would space the stud wall off of the block wall.